1. Field of the Invention.
This invention relates to aircraft speed control systems and, more particularly, to such systems for eliminating air speed overshoot problems which arise under particular flight conditions.
2. Description of the Prior Art.
Certain aircraft speed reference systems in present use on large commercial and military aircraft, such as passenger liners and cargo planes, employ a longitudinal acceleration damping (anticipation) signal which is derived from the difference between an accelerometer signal and a vertical gyroscope pitch attitude signal. (In certain systems a pendulum may be used as the source of the accelerometer signal. For the purpose of describing the present invention, it will be understood that this type of sensor is to be included in references to an accelerometer signal.) The accelerometer is mounted in the aircraft to be sensitive to longitudinal motion of the aircraft. Air speed overshoot is observed when using such prior art speed reference systems to capture and control the aircraft to a predetermined air speed after a long term deceleration from a much higher air speed. Such overshoot is undesirable to the extent that it may exceed the five-knot speed holding accuracy prescribed by the FAA for certain landing approach operations.
The undesirable air speed overshoot which is presently encountered in existing systems may be explained by considering that during a long term deceleration, the vertical gyro erection mechanism will cause the vertical gyro to slowly erect to the apparent vertical attitude as determined by the gyroscope levelling devices mounted on the inner platform of the vertical gyro. Such devices are inherently responsive to the effect of acceleration forces on the apparent gravity vector. A pendulum, which is used for detecting longitudinal acceleration, always aligns itself with the apparent vertical direction and a longitudinal accelerometer always has an output equivalent to the apparent vertical deviation from the true vertical, both indications being in addition to the actual pitch attitude. As the vertical gyro slowly erects to the apparent vertical direction (assuming zero degrees actual pitch attitude) an acceleration signal which is derived from the difference between the vertical gyro and the pendulum or accelerometer eventually goes to zero.
Approximate equations for the pendulum and for an accelerometer whose sensitive axes are longitudinal with respect to the aircraft are as follows: EQU .theta..sub.P = .mu./g + sin.theta..sub.T = .mu./g + .theta..sub.T * (1) EQU a.sub.x = .mu. + gsin.theta..sub.T = .mu. + g.theta..sub.T * (2) EQU a'.sub.x = .mu./g + sin.theta..sub.T = .mu./g + .theta..sub.T * (3)
where:
.theta..sub.P = pendulum angle (in degrees) from axis vertical to longitudinal PA1 .theta..sub.T = true pitch attitude PA1 .mu. = acceleration of aircraft along flight path PA1 g = gravitation constant (32.2 ft/sec.sup.2) PA1 A.sub.x = Accelerometer output (ft/sec.sup.2) PA1 A'.sub.x = Accelerometer output (in radians) FNT * for small angles such that sin.theta..sub.T approximates .theta..sub.T. PA1 .mu..sub.d = the derived acceleration (in radians). PA1 Spc = speed command to pilot or automatic throttle (+ means to move throttles forward) PA1 Spderr = airspeed or other preselected parameter error (+ means overspeed) PA1 .mu..sub.d = derived acceleration (+ means accelerating)
The derived acceleration signal for a perfect vertical gyro where .theta..sub.T = .theta..sub.VG, the attitude of the aircraft as measured by the vertical gyro, may be expressed as follows: EQU .mu..sub.d = .theta..sub.P - .theta..sub.VG = .mu./g + .theta..sub.T - .theta..sub.T = .mu./g (4)
where
In the case where an imperfect, or miss-erected, vertical gyro is used, the output of the vertical gyro is as follows: EQU .theta..sub.VG = .theta..sub.T + .mu./g (5)
The .mu./g term results from the gyro erecting to the apparent vertical direction where the deviation of apparent vertical from true vertical is equal to the acceleration term affecting the levelling device or accelerometer inside the vertical gyro erection mechanism.
The derived acceleration signal for the imperfect vertical gyro which has sufficient time to fully miss-erect then becomes: EQU .mu..sub.d = .theta..sub.P - .theta..sub.VG = .mu./g + .theta..sub.T - .theta..sub.T - .mu./g = 0 (6)
Thus it may be seen that the derived acceleration term goes to zero under such conditions when in fact the aircraft is still decelerating. Furthermore, when the aircraft stops decelerating, the imperfect or miss-erected vertical gyro takes some substantial time to re-erect and the .mu./g term is initially retained, thus producing a false derived deceleration signal until the gyro has time to correctly erect itself, a period of approximately one to two minutes.
Using Equation (5) for the miss-erected vertical gyro, the equation for deriving the acceleration signal under a condition of no acceleration is: EQU .mu..sub.d = .theta..sub.P - .theta..sub.VG = .theta..sub.T - .theta..sub.T - .mu./g = -.mu./g (7)
The .mu./g term in Equation (7) is the miss-erection term from the vertical gyro which goes to zero in approximately 1 to 2 minutes. The speed overshoot can be shown to be caused by the erroneous acceleration term derived in Equation (7). An equation for a speed reference system using a speed error term (which is preferably a function of air speed or angle of attack but may also be developed from a lift sensor or some other parameter detector) and a derived acceleration term is as follows: EQU SPC = -(SPDERR + .mu..sub.d) (8)
where:
Equation (8) shows absence of command to move the throttles when the term SPC is equal to zero. If .mu..sub.d is erroneous, as indicated in Equation (7), due to a long term deceleration, the initial no acceleration case finds .mu..sub.d position and equal to -.mu./g. (For a deceleration, .mu. is negative, making the term "-.mu./g" positive). The speed command term SPC from Equation (8) will only be zero, indicating no command to move the throttles, when the SPDERR term is negative or slow (which causes the overshoot that is encountered in the aircraft instrumentation system following a long term deceleration).
There have been attempts to solve the speed overshoot problem discussed above. One such attempt has involved the provision of an attempted compensation signal which is operative upon detection of the fact that the aircraft is decelerating. This proposed solution to the problem utilizes a filter in series with the deceleration detector to develop an additional slowly changing signal for the desired compensation. However, this attempted solution method is deficient during long term decelerations in which the derived acceleration term .mu..sub.d of Equation (8) goes to zero, with the result that the compensation signal from the added filter slowly returns to zero while the aircraft is still decelerating. Under such conditions, the effects of the gyro miss-erection on the derived acceleration signal are no longer cancelled and the aircraft will overshoot the desired air speed as before. Clearly this is not a solution but a mere alleviation of the problem.